There isn't a definite order near the end, but this is about the set of subject areas you'll need to cover: I can go ahead and tell you that although calculus does provide some motivation for linear algebra, it is not necessary for it also, there are no formal prerequisites for topology, but you will need this nebulous thing called "mathematical maturity" to understand it, which is why it is not offered until late in college or early in graduate school (although the rudiments of point-set topology are used in "Introductory Analysis" or "Advanced Calculus"). The resources I'm familiar with are in English (including this set of miniature teaching units covering the techniques of mathematics required by engineering students, starting with a review of Basic Algebra and ending with Ordinary Differential Equations, Numerical Analysis, Probability, and Introductory Statistics), but there may be related resources in your language.Īlso, I'm surprised that any high school teaches differential equations, and very few in my country (United States) even teach linear algebra or multi-variable calculus. There is a wide variety of free PDF textbooks of mathematics in all of these areas, and I might get around to giving a list, but I am curious about what country you live in and what your native language is.
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